Question: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{r^2 + 7r + 6}{r^2 + 6r}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{r^2 + 7r + 6}{r^2 + 6r} = \dfrac{(r + 1)(r + 6)}{(r)(r + 6)} $ Notice that the term $(r + 6)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(r + 6)$ gives: $n = \dfrac{r + 1}{r}$ Since we divided by $(r + 6)$, $r \neq -6$. $n = \dfrac{r + 1}{r}; \space r \neq -6$